Open systems can be described effectively by non-Hermitian Hamiltonian. Recently, non-Hermitian topological theories have been introduced and experiments have been conducted in dozens of open systems [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}.
Many interesting features are predicted and observed in non-Hermitian systems, including the band defined on the complex plane [4]}, the breakdown of the conventional bulk-boundary correspondence [5]}, [6]}, [7]}, [8]}, [9]} and the non-Hermitian skin effect [5]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}. The definition of the topological invariance for non-Hermitian systems has also been discussed [4]}, [23]}.
